Method and apparatus for locating well casings from an adjacent wellbore

ABSTRACT

A wellbore tool for locating a target wellbore containing a conductive member from a second wellbore and directing the trajectory of the second wellbore relative to the target wellbore includes an electric current driver having an insulated gap; a three-axis magnetometer positioned within a non-magnetic housing that is disposed within a non-magnetic tubular, the three-axis magnetometer positioned below the electric current driver; a drill bit positioned below the three-axis magnetometer; a hollow tubular connected between the electric current driver and the three-axis magnetometer; and a measurement-while-drilling tool. The current driver generates an electric current across the gap to the portion of the tool below the insulated gap. In a method a current is generated across the insulated gap to the portion of the tool below the insulated gap to the conductive material in the target wellbore returning to a portion of the bottom hole assembly above the insulated gap thereby producing a target magnetic field. Measuring the target magnetic field at the bottom hole assembly and the earth&#39;s magnetic field; and determining the position of the second wellbore relative to the target wellbore. Then steering the bottom hole assembly to drill the second wellbore along a trajectory relative to the target wellbore.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 60/733,347 filed on Nov. 4, 2005.

FIELD OF THE INVENTION

The present invention relates in general well drilling operations andmore particularly to locating a casing or drill string of a firstwellbore from a second wellbore while drilling the second wellbore.

BACKGROUND

In various drilling operations it is desirable to locate adjacentwellbores. Examples of drilling operations which may require locatingadjacent wellbores, include relief drilling, drilling U-shaped wells,and steam assisted gravity drainage (SAGD). From time to time wellsblowout and it is desired to kill the well subsurface, thus it isnecessary to accurately position the first well while drilling thesecond intercepting relief wellbore. Currently, a common application forlocating adjacent wellbores occurs when drilling a second wellboresubstantially parallel to a first wellbore such as in SAGD wells.

Current methods for locating casing (or drill string) of a firstwellbore use wireline tools. Conducting locating surveys utilizingwireline tools, and relying on those results, has significant drawbacks.For example, using wireline equipment increases rig time and costs.Further, wellbore location information is only obtained periodicallywith these wireline methods. This unavailability to have constant,timely and accurate data can result in significant and costly errors.

Therefore, it is a desire to provide an adjacent well locating deviceand method that addresses drawbacks of the prior art locating devicesand methods. It is a still further desire to provide an adjacent welllocating device and method with measurement while drilling (“MWD”).

SUMMARY OF THE INVENTION

An embodiment of a wellbore tool for locating a target wellborecontaining a conductive member from a second wellbore is provided. Thewellbore tool includes an electric current driver having an insulatedgap and at least one magnetometer positioned above or below the electriccurrent driver. The electric current driver generates an electriccurrent across the gap to the portions of the tool above and below theinsulated gap.

In another embodiment, a wellbore tool for locating a target wellborecontaining a conductive member from a second wellbore and directing thetrajectory of the second wellbore relative to the target wellboreinclude an electric current driver having an insulated gap; at least onemagnetometer, the magnetometer positioned above or below the electriccurrent driver; a drill bit positioned below the magnetometer; a hollowtubular connected between the electric current drive and themagnetometer; and a measurement-while-drilling tool. The current drivergenerates an electric current across the gap to the portions of the toolabove and below the insulated gap.

An embodiment of a method of locating a target wellbore containing aconductive member from a second wellbore and directing the trajectory ofthe second wellbore relative to the target wellbore is provided. Themethod includes the steps of providing a bottom hole assembly having anelectric current driver with an insulated gap, at least one magnetometerpositioned above or below the electric current driver, and a drill bitpositioned below the magnetometer; drilling a second wellbore spacedfrom the target wellbore with the bottom hole assembly; producing a lowfrequency current flowing from the current driver; measuring the targetmagnetic field at the bottom hole assembly; and determining from thetarget magnetic field measurements the position of the second wellborerelative to the target wellbore.

The foregoing has outlined the features and technical advantages of thepresent invention in order that the detailed description of theinvention that follows may be better understood. Additional features andadvantages of the invention will be described hereinafter which form thesubject of the claims of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and aspects of the present inventionwill be best understood with reference to the following detaileddescription of a specific embodiment of the invention, when read inconjunction with the accompanying drawings, wherein:

FIG. 1 is a schematic of an embodiment of a wellbore locating system ofthe present invention;

FIG. 2 is a cross-sectional view of an embodiment of a wellbore locatingtool revealing a magnetometer;

FIG. 3 is a schematic of an embodiment of a data acquisition sequence;

FIG. 4 is a cross-sectional view of a wellbore locating tool at themagnetometer illustrating magnetic fields with an asymmetric drillcollar;

FIGS. 5A-5D are illustrations of the magnetometer at various rotatedpositions and the associated average magnetic field measurements;

FIG. 6 is a schematic a plan view of a target casing and the trajectoryof a second wellbore;

FIG. 7 is a schematic illustrating the drilling of a first wellbore infor SAGD operations; and

FIG. 8 is a schematic illustrating the drilling of a second wellborerelative to the first wellbore of FIG. 7.

FIG. 9 is a schematic illustrating one example of drilling a SAGD wellabove a cased well showing the direction of current flow.

FIG. 10 is a drawing show example orientations of two SAGD wells and theangles between them.

FIG. 11 is a schematic showing an example where the axes of two wellsand the radial vector between them.

FIG. 12 is a schematic showing one example of the axes of two wells andthe radial vector between them when the second well is directly abovethe first well.

FIG. 13 is a plot of (tan γ₀ cos θ−sin θ) as a function of θ for tanγ₀=−0.4, 0, +0.4.

FIG. 14 is a plot of the magnetic field components for the example whena second well is parallel to a first well and there are inter-wellspacing of 5 m and 10 m. Also shown are the magnetic field componentswhen the first is not present.

FIG. 15 is a plot of the magnetic field components for the example whena second well is tiled at an angle φ with respect to a first well andwith an inter-well spacing of 5 m.

DETAILED DESCRIPTION

Refer now to the drawings wherein depicted elements are not necessarilyshown to scale and wherein like or similar elements are designated bythe same reference numeral through the several views.

As used herein, the terms “up” and “down”; “upper” and “lower”; andother like terms indicating relative positions to a given point orelement are utilized to more clearly describe some elements of theembodiments of the invention. Commonly, these terms relate to areference point as the surface from which drilling operations areinitiated as being the top point and the total depth of the well beingthe lowest point.

FIG. 1 is a schematic of an embodiment of a wellbore locating system 10that includes a bottom hole assembly (“BHA”) 12 that is equipped tolocate a target wellbore 14 in earthen formation 5 while the BHA 12 isused to drill a second wellbore 16 in formation 5, such that secondwellbore 16 may be positioned as desired and guided along a desiredtrajectory. Target wellbore 14 has been completed with target casing 18.

In the example shown in FIG. 1, BHA 12 includes a drill bit 20,steerable system 22, a magnetometer tool 24 with a three-axismagnetometer 6, and an electric current driving tool 28 having aninsulated gap 30 in operational connection with one another. PreferablyBHA 12 further includes at least one drill collar 27 positioned betweenthree-axis magnetometer tool 24 and current driving tool 28. BHA 12 isrun on drill pipe 32. It is noted that BHA 12 may further includelogging-while-drilling (LWD) tools, measurement-while-drilling (MWD)tools, telemetry tools, as well as other downhole tools for use in adrilling environment. It is also noted that a magnetometer tool mayinclude other sensors, such as accelerometers.

Electric current driving tool 28 may be, for example, Schlumberger'sE-Pulse or E-Pulse Express (add reference patent). For purposes ofbrevity, current driving tool 28 may be referred to herein as E-Pulse28, although other current driving tools may be utilized withoutdeparting from the scope of the claimed invention. In the illustratedembodiment, the magnetometer tool 24 includes measurement-while-drilling(MWD) and telemetry (mud pulse or electromagnetic) components. It isnoted that in some operations, a different configuration may be used.For example, in one example, the current driving tool may be anelectromagnetic telemetry tool. In another example, a BHA 12 may includea mud pulse telemetry tool and a current driving tool.

FIG. 2 is a cross-sectional view of one example of a magnetometer tool24 with three-axis magnetometer 26. Three-axis magnetometer 26 ispositioned within a drill collar 34, which may be constructed of anon-magnetic metal such as stainless steel or beryllium copper; both ofwhich are commonly used as drill collar material. The wall thickness ofdrill collar 34 is typically an inch or greater. Three-axis magnetometer26 may be carried in a non-magnetic pressure housing 36 centered withindrill collar 34. A channel 38 is provided between pressure housing 36and the interior wall of drill collar 34 for drilling mud.

With reference to FIGS. 1 and 2, current driving tool 28 generates anelectric current 40 a across insulated gap 30. For example, electriccurrent 40 a may have a frequency between about 1 Hz and about 100 Hz,and with amplitude up to about 17 amps. Current 40 a flows along BHA 12and enters formation 5, shown as current 40 b. In oil-based mud (OBM),most of current 40 a will leave through drill bit 20 and will return toBHA 12 as current 40 d above insulated gap 30 through stabilizers (notshown) and drill pipe 32 in contact with the wall of wellbore 16. Inwater-based mud (WBM), current 40 a will flow out of BHA 12 along itslength as current 40 b. Current 40 a decreases in an approximatelylinear manner between insulated gap 30 and drill bit 20 in WBM. Whencasing 18 is adjacent to BHA 12, some of current 40 b will concentrateon casing 18, shown as current 40 c, and return to the upper portion ofBHA 12, shown as current 40 d, after traveling along casing 18.

Target casing 18 provides a very low resistance path compared toformation 5, as the conductivity of casing is typically six orders ofmagnitude greater than formation conductivity. For example, theresistance of 9-⅝ inch casing is roughly equivalent to a cylinder of 1ohm-m formation with a diameter of 500 feet. This high contrast resultsin much more current returning on the casing than in the formation whencasing 18 is near tool 12.

Electric current 40 c on casing 18 produces magnetic field B ₁, which isan azimuthal magnetic field centered on target casing 18. The presenceof magnetic field B ₁ indicates that target casing 18 is nearby, and theintensity and orientation of magnetic field B ₁ can be used to estimatethe direction from BHA 12 to target casing 18 and thus wellbore 14.

Current 40 c on target casing 18 will be weaker than current 40 a on BHA12, but will have the same frequency and be in phase with it. Withcurrent 40 c represented I′, azimuthal magnetic field B ₁ centered ontarget casing 18 is given approximately by Eq. 1:

$\begin{matrix}{{{\overset{\_}{B}}_{1}(z)} = {\frac{\mu_{0}I^{\prime}}{2\;\pi\; r}\overset{\bullet}{\psi}}} & \left( {{EQ}.\mspace{14mu} 1} \right)\end{matrix}$

Where μ₀=4π·10⁻⁷ Henry/m, r is the radial distance (m) from targetcasing 18 at axial location z to BHA 12, and ψ is the unit vector in theazimuthal direction. Measuring magnetic field B ₁ provides informationabout the direction and distance of target casing 18 relative to BHA 12.

Magnetic Field B ₁ from target casing 18 will penetrate drill collar 34and pressure housing 36 provided the frequency is sufficiently low. Theskin depth in a metal with conductivity σ and magnetic permeability μ′is given by Eq. 2, where f is the frequency.δ=(π^(fμ′μ) ₀σ)^(−1/2)  (EQ. 2)

For example, non-magnetic steel (μ′=1) used in drill collars typicallyhas a conductivity σ=1.4/10⁶ S/m. At 10 Hz, the skin depth is 5.3 inches(0.13 m), so magnetic field B ₁ can reach magnetometer 26 forfrequencies of 10 Hz and lower with very little attenuation.

Magnetic field B ₁ will be perpendicular to a radius from target casing18 to the point of observation, i.e. magnetometer 26. Hence, byanalyzing magnetic filed B ₁, three-axis magnetometer 26 can be utilizedto determine a direction that either points toward or away from targetcasing 18. Provided that the distance to target casing 18 is less than askin depth in formation 5, magnetic field B ₁ will be in phase with thesource current 40 a. This condition is easily met since the skin depthin a 1 ohm-m formation is 5200 feet (1.6 km) at 10 Hz.

In FIG. 1, target casing 18 is located to the left of second wellbore 16and BHA 12 and the current 40 a flows down in BHA 12. This result in amagnetic field pointing into the page at three-axis magnetometer tool24. If target casing 18 were located to the right of BHA 12, thenmagnetic field B ₁ would point out of the page. Thus, the direction ofmagnetic field B ₁ can be used to resolve the direction to target casing18.

FIG. 3 is a schematic illustrating one example of a data acquisitionsequence. Signal 42 represents an electric current that is cycled off,and then cycled on in two periods in which the current reversespolarity. Signal 42 may be used to drive electric current 40 a throughlocating tool 12. FIG. 3 assumes BHA 12 is stationary during dataacquisition for purposes of description, however target casing 18 may belocated and positioned relative to BHA 12 while drilling wellbore 16 andthus with BHA 12 moving, for example, it may be rotating.

Signal 42 has a magnitude of zero between the time interval (0, T),which is shown in FIG. 3 as a first time interval between time 0 andtime T. During time interval (T, 2T), signal 42 is “on” with a magnitudeof I(t)=Io. Time interval (T, 2T) is a second time interval betweentimes T and 2T. During the time interval (2T, 3T), which is a third timeinterval between time 2T and time 3T, signal 42 is “on” with a negativemagnitude of I(t)=−Io. The corresponding magnetic field vectors measuredby the magnetometer during these three periods are shown in the upperportion of FIG. 3.

For the first time interval, which is the interval between time 0 andtime T, magnetometer 26 senses vector B _(e), which represents theEarth's magnetic field. Since magnetometer 26 is a three-axismagnetometer, vector B _(e) contains information regarding the spatialorientation and magnitude of the magnetic field in which magnetometer 26is immersed. In the second time interval between time T and time 2T,magnetometer 26 senses a vector representing the sum of the Earth'smagnetic field and magnetic field B ₁. The vector sensed during thesecond time interval is shown in FIG. 3 as vector B ₁ and is given by B₁= B _(e)+ B ₁. In the third time interval between time 2T and time 3T,magnetometer 26 senses vector B′_(t), which is the magnetic fieldresulting from reversing the direction of current 40 a. Vector B′_(t) isrepresented by the equation B′_(t)= B _(e)− B ₁.

Using data acquired by magnetometer 26 during the three time intervalsshown in FIG. 3, magnetic field B ₁ from target casing 18 can becalculated. Magnetic field B ₁ from target casing 18 can be obtained byaccounting for the effect of the Earth's field, vector B _(e), in eithervector B _(t) or vector B′_(t). Alternatively, magnetic field B ₁ can bedetermined by the equation: B ₁=( B _(t)− B′_(t)). Note that it is notnecessary for source 28 producing electric current 40 a to produceexactly the same amplitudes for positive and negative polarities, sincethe direction of B ₁ is more important than its amplitude, and itsdirection does not depend on the amplitude of the current, but on therelative positions of locating tool 12 and target casing 18.

In one example, the time period, T, may have a duration ranging between10 milliseconds and 10 seconds, depending on the time required for agood signal to noise ratio regarding measurements by magnetometer 26.The signal strength depends on several factors, including the amplitudeof electric current 40 a, the distance between target casing 18 and BHA12, whether target casing 18 and BHA 12 are parallel, the electricalresistance of formation 5, the electrical resistance of the mud, and theelectrical resistance of the contact between BHA 12 and formation 5 inoil-based mud. Any noise depends on properties of magnetometer 26 andits electronic components, the integration time, and any parasiticsignals that may arise from any imperfections on electronics associatedwith target causing 18 or BHA 12, from tool vibration in the Earth'smagnetic field, or from the magnetic field on BHA 12 due to electriccurrent 40 a.

Let I(z) be the axial current 40 a at the location of magnetometer 26,where z is the axial distance from the gap. This current produces anazimuthal magnetic field Bo(z), shown in FIG. 2. Calculations regardingmagnetic field B ₀(z) can be performed if the axial current isrepresented as I(z), drill collar 34 has an inner radius of r=a, anddrill collar 34 has an outer radius of r=b. At r=b, the axial currentI(z) produces an azimuthal magnetic field given by

${{{\overset{\_}{B}}_{0}(z)} = {\frac{\mu_{0}{I(z)}}{2\;\pi\; b}\hat{\theta}}},$where {circumflex over (θ)} is the unit vector in the azimuthaldirection. Since I(z)>1′ and d□b, hence | B ₀|□| B ₁|. It is importantthat magnetometer 26 be insensitive to magnetic field B ₀.

If drill collar 34 and pressure housing 36 of magnetometer tool 24 arecylindrically symmetric, the axial current I(z) will also becylindrically symmetric. This axial current will penetrate into thecross-sectional area of the drill collar, and a cylindrically symmetriccurrent density J(r)=J(r){circumflex over (z)} can be defined with unitsof amps/m², where {circumflex over (z)} is the unit vector inz-direction. By cylindrical symmetry, we mean that J(r) is not afunction of the azimuth angle θ. If J(r)=0 for r<a, then the magneticfield will also be zero for r<a everywhere inside the drill collar. Thisfollows from Maxwell's equations for electromagnetism and by evaluatingthe integrals ∫ B·d t=μ_(e)∫∫ J(r),zdxdy where the left-hand lineintegral is evaluated over a circle of radius r<a and the right-handarea integral is evaluated over the cross-sectional area of that circle.This result does not hold true if J(r)≠0 anywhere inside the drillcollar 34. Thus, it is important that none of electric current 40 a beallowed inside the drill collar 34 via wires, feed-throughs, or otherpaths. In particular, there should be no hard-wired connection, such ason an internal bus, between the internal parts of the current driver 28tool and magnetometer tool 24. Further, there should preferably be atleast one hollow section of drill collar 27 between current driving tool28 and magnetometer tool 24.

As illustrated in FIG. 4, if there is a slight asymmetry in drill collar34, then it is possible that a weak secondary magnetic field, such asparasitic field B ₂, could penetrate magnetometer 26. The localizedfields potentially influencing magnetometer 26 can be modeled as acylindrically symmetric field B ₀ plus a much smaller asymmetricparasitic field B ₂ which is a function of θ and r. Parasitic field B ₂arises from a magnetic dipole source, for example from a hole throughdrill collar 34 (H. A. Bethe, Phys. Rev. 66, p 163, 1944).

The parasitic field B ₂ can be accounted for and removed from the datawith the following procedure, if parasitic field B ₂ is not too largecompared to magnetic field B ₁. First, assume that the Earth's magneticfield has been removed using the alternating current method describedabove in conjunction with FIG. 3. After this process, as illustrated inFIG. 5, the residual magnetic field B _(s) is the sum of magnetic fieldB ₁ and parasitic field B ₂, given by the equation B _(s)= B ₁+ B ₂.

In FIG. 5A through 5D, the bottom views represent three-axismagnetometer 26 (tool 24) of FIG. 4 rotated to four separate angles 0°,90°, 180° and 270° respectively. These are known as the toolface angleor θ_(TF). The toolface angle refers to the orientation of themagnetometer 26, and not to the source of the asymmetric field B ₂. Thetool face angle is measured with respect to gravity, as determined usingaccelerometers mounted in the magnetometer field B _(s) generated at thecorresponding angles. Note that the orientation of parasitic field B ₂,depends on the orientation of the drill collar 34, while the magneticfield B ₁ is constant in direction and amplitude. Accordingly, if theresidual field is obtained as a function of the orientation of the drillcollar 34 (or toolface), then parasitic field B ₂ can be removed viasignal processing. A simple exchange is shown in FIGS. 5A through 5Dwhere the residual magnetic fields B _(s)(0), B _(s)(90), B _(s)(180)and B _(s)(270) is measured at four angles 0°, 90°, 180°, and 270°respectively. The average of these four readings eliminates parasiticfield B ₂, and magnetic field B ₁ is given by B ₁={ B _(s)(0)+ B_(s)(90)+ B _(s)(180)+ B _(s)(270)}/4.

It is not necessary to make the measurements at the particular anglesillustrated in FIGS. 5A through 5D, a few measurements at random anglesare sufficient so long as they are distributed around 360° of toolface.It is clear that the parasitic magnetic field for random angles forms acircle centered on the casing magnetic field. Simple trigonometry couldthen be used to solve for magnetic field B ₁ using the known values forthe toolface at each sample B _(s)(θ_(TF)).

Alternatively, if drill collar 34 is rotating smoothly, it is possibleto acquire continuous measurements from magnetometer 26. If the magneticfield readings are averaged over several drill collar 34 rotations, thenthe parasitic field B ₂ will average to zero. The toolface may beobtained from accelerometers, provided the drilling shocks are not toogreat. Hence, a potential procedure is to average the readings overseveral rotations with the source current with positive polarity, thenaverage the readings with the opposite polarity of the source current.Let these two averages be

B _(t)

, then the magnetic field B ₁ is given by B ₁={

B _(t)

−

B′_(t)

}. The difference in the last equation removes the Earth's magneticfield component.

Intercepting an exiting wellbore with a second well is used for killingblow-outs and for drilling “U-shaped wells”. In a blow-out, the firstwell encounters an unexpectedly high pressure formation during drilling.If the weight of the drilling mud is too low, the formation pressureexceeds the borehole pressure and fluids from the formation enter thewellbore in an uncontrolled manner. The formation fluids blow thedrilling mud out of the annulus between the formation and the drillstring. Since the formation fluids are less dense than the mud, thepressure at the surface can become very high. This is a serioussituation that may endanger people and the environment and that maydamage the drilling rig and the reservoir. If standard drilling controlmethods (e.g. “weight and wait”) cannot reestablish a greater pressurein the borehole than in the formation, the extreme measure of drilling arelief well is undertaken. A second wellbore is drilled from an offsetlocation and attempts to intercept the first well a short distance abovethe blown-out formation. Wireline magnetic ranging methods are usedwhere the drilling BHA in the second well is periodically removed and awireline tool is run in the open hole of the relief well (see U.S. Pat.No. 4,732,398). The wireline tool of U.S. Pat. No. 4,732,308 has twowidely spaced, current injecting electrodes, and a sonde with amagnetometer located midway between them. The injected currentconcentrates on the drill string in the first well, and the resultingmagnetic field is measured with the magnetometer to determine therelative bearing of the first well with respect to the second well. Bytaking several bearings at different locations in the relief well, it isalso possible to determine the distance to the blow-out. Eventually, therelief well is able to intercept the blow-out, but this may require alarge number of trips, i.e. the drill string is removed and a wirelinemagnetic ranging tool is run into the open hold. Each trip may requireone or more days of rig time, so the process can be very slow andexpensive. The relief well has a very heavy mud that can “kill” theblow-out by reestablishing a borehole pressure greater than theformation pressure.

As the process of determining the relative bearing and distance totarget casing from a wellbore is known in the art for wireline magneticranging, it is therefore briefly described with reference to FIG. 6 forBHA 12. FIG. 6 provides a plan view of the trajectory or path of secondwellbore 16 and target casing 18. BHA 12 (not shown) is positionedwithin wellbore 16 and the distance to target casing 18 is determinedvia triangulation. The target casing magnetic field B ₁ induced bycurrent in the target casing 18 is measured at various locations withmagnetometer 26 in BHA 12 while wellbore 16 is being drilled. As isevident from the description of the present invention with reference toFIGS. 1 through 5, BHA 12 may be utilized to both drill wellbore 16 andto measure magnetic field B ₁. Utilizing the various readings of casingmagnetic field B ₁, at various angles relative to target casing 18, thedistance between the two wells may be simply calculated usingtriangulation.

Prior to the present invention, it was necessary to pull the BHA out ofthe wellbore and run a wireline magnetic ranging tool to locate thetarget casing. Then go back in the wellbore with the BHA to continuedrilling operations. System 10 of the present invention may facilitatetracking the location of target casing 18 relative to wellbore 18without removing the BHA from the wellbore, thus significantly reducingtime, costs and improving the accuracy in drilling the second wellbore.

A second application for intercepting a first wells from a second wellis to create a “U-shaped” well. Two horizontal wells are drilled fromdifferent locations and intercept “toe-to-toe” underground) see “FirstU-tube well connects horizontal wells”, Drilling Contractor,September-October 2005). One purpose for drilling a U-shaped well is tolay cables or pipelines under a river. Another purpose is to provide apipeline from land to an offshore well, where the stability of theseafloor cannot support a seafloor pipeline. Another purpose may be toproduce heavy oil through hot subsurface formations, rather than througha seafloor pipeline exposed to cold water. Cold pipelines increase theviscosity of the heavy oil and may prevent its production. To drill aU-shaped well, a first well is drilled and cased. As the second well isdrilled and approaches the end of the first well, a wireline tool mustbe inserted in the first well for magnetic ranging. This requires a rigbe maintained on the first well to deploy the wireline tool in thehorizontal well.

An example of a method of operating wellbore locating system 10 is nowdescribed with reference to FIGS. 1 through 5. There are severalpossible strategies for activating the data acquisition process and onesuch process is described herein. Typically, drilling of second wellbore16 proceeds slowly (˜50 ft/hr) and the distance and direction of targetcasing 18 relative to wellbore 16 does not change rapidly. Therefore,there may be no need or desire to continuously measure the relativebearing to target casing 18.

Upon initiation of the data acquisition sequence, current driver 28cycles current 40 a off, current 40 a on, and current 40 a reversed witha predetermined time interval T. In one example, the method is conductedas shown in FIG. 3. Similarly, MWD tool 24 may begin the measurementsequence when it detects the initiation of the acquisition sequence.Magnetometer 26 initially reads the Earth's magnetic field if a casingis present. When current 40 a is reversed, magnetometer 26 will againdetect the change in magnetic field. Without a direct communication andsynchronization path between current driver 28 and MWD tool 24, the MWDtool will deduce the periods of off, on, and reversed current. This canbe done by correlating the magnetometer data to the know timingsequence. For example, the previously described sequence was current offfor the first time interval (0,T) current on for the second timeinterval (T, 2T), and current reversed for the third time interval (2T,3T). This could be repeated for a predetermined number of cycles. TheMWD tool 24 would then compute the cross-correlation between the currentprofile and the magnetometer data to obtain three values of the magneticfield. Using unequal periods, for example, current off during (0, 2T),current on during (2T, 3T), and current reversed during (3t, 4T) wouldunambiguously mark the current off, on, and reversed periods. Sincecurrent driver 28 may be programmed to begin the current with a knownphase (e.g. positive), there would be no ambiguity about the sign of thedirection toward the casing.

Once the data has been processed to obtain Earth's magnetic field ( B ₀)and Bs(θ_(TF)), where θ_(TF) is the toolface, MWD tool 24 can transmitthis information to the surface. The BHA can then be rotated and stoppedat another toolface angle, and the process repeated to obtain anotherreading, Bs(θ′_(TF)) at the new toolface angle. If no parasitic magneticfield B ₂ is detected, then it may not be necessary to take measurementswith multiple toolface angles.

Wellbore locating system 10 of the present invention is of particularinterest for steam assisted gravity drainage (SAGD) productionoperations. SAGD requires at least two horizontal wells to be drilledparallel to each other. One well is positioned directly above the otherwell, and typically with a constant separation, for example of 3 to 5meters. These wells can be completed with casing or slotted liners. Oncethe wells are completed, steam is injected in the upper well and thehydrocarbons are produced from the lower well.

An embodiment of a method of drilling a first well 14 and a second well16 for SAGD operations is now described with reference to FIGS. 1through 8. Referring to FIG. 7, first horizontal wellbore 14 is drilledusing established techniques developed for geosteering wellboresparallel to an interface, such as the heavy oil-shale interface 52. Thedrilling assembly, shown as BHA 54 typically includes a drill bit 20, asteerable system 22, LWD system 56 (containing, for example, tools formeasuring resistivity, gamma-ray, sonic, and/or nuclear tools), and anMWD system 58 to provide direction, inclination, and telemetry, forexample. LWD system 56 may include Schlumberger's PeriScope15 or asimilar system, that can measure the formation resistivity up to about15 ft away from the BHA; the formation resistivity azimuthally aroundthe BHA; and it can determine vertical and horizontal resitivities ifthe formation is anisotropic. LWD 56 may measure the resistivity at bit20 and provide high resolution images of the borehole wall, which mayprovide information about fine bedding. The LWD 56 resistivity tools mayprovide an extremely detailed map of the formation resistivity in arelatively large volume surrounding the wellbore. Wellbore 14 iscompleted with casing 18.

As illustrated in FIG. 8, second wellbore 16 is drilled directly above(or below) first wellbore 14 using BHA 12 that includes a locating tool.BHA 12 is described with reference to FIGS. 1 and 2 and may furtherinclude a LWD system 56. As previously described, electric current 40induces magnetic field B ₁ around target casing 18. Magnetic field B ₁may be analyzed to determine the direction and distance of target casing18 relative to tool 12. For SAGD operations it is desired to maintainsecond wellbore 16 a substantially constant distance S from targetcasing 18. Thus, triangulation, which requires undulating the trajectoryof wellbore 16, may not be desired. Therefore, alternative methods fordetermining and maintaining separation distance S are provided.

An example of an algorithm is now presented to illustrate how the secondSAGD well can be positioned with respect to the first well based onmagnetic field measurements. Normally, the first well drilled is thelower, producing well 14 (see, e.g., FIG. 7). After the first well 14has been cased, the upper, second well 16, also called an injector well,is drilled parallel to the first well (FIG. 9). As shown in FIG. 9, thesecond well 16 is drilled using a BHA 22 that includes a drill bit 20, asteerable system, 22, an LWD tool 56, and a three-axis magnetometer 58.

FIG. 10 shows the relative bearings of the two wells and the angels thatrelate the two wells. The (x,y,z) coordinate system is associated withthe second well, where {circumflex over (z)} is a unit vector alignedwith the borehole axis and pointing toward the drill bit. The unitvector {circumflex over (x)} points downward (in the direction ofgravity). The {circumflex over (x)} direction can be determined from theaccelerometers in the MWD tool used in drilling the second well. Thefirst well is aligned with the unit vector {circumflex over (n)}. Theangle between the two wells is φ and the projection of {circumflex over(n)} into the (x,y,0) plane forms an angle θ with respect to the x-axis.In one example, the second well 16 is directly above the first well 14.

Let the insulated gap 30 in the BHA 22 in the second well be located atz=0, and the bit be located at z=L, where L is the length of the BHAbelow the insulated gap. A current I(0) is generated across theinsulated gap 30 in the second well 16 and flows along the BHA 22 in thesecond well 16, denoted as I(z). In electrically conductive water basedmud (WBM), the current I(z) decreases approximately linearly withdistance from the insulated gap 30 and goes to zero at the bit face, sothat I(z)≈I(0)·(L−|x|)/L between the insulated gap 30 and the drill bit20. Above the insulated gap 30, the current also decreases in a linearmanner, but extends further up the drill string. In electricallyinsulating oil based mud (OBM), the current I(z) remains constant belowthe insulated gap 30, and enters the formation only through the face ofthe drill bit 20. In OBM, the current below the insulated gap is givenby I(z)≈I(0). The current returns to the BHA above the gap throughstabilizers and through drill collar contact with the formation.

In either case of WBM or OBM, most of the current leaving the BHA in thesecond well 16 flows to the first well 14, and then returns along thetarget casing 18. Let the current on the target casing 18 be denoted asI′. In OBM, the current on the casing will be relatively constant alongits length, and given by I′≈−I(0). In WBM, the current will vary alongthe casing as I′≈−I(z) if the separation of the two wells is smallcompared to L. The current generated across the insulated gap 30, I(0),is measured and transmitted to the surface in real time. Depending onwhether the second well 16 is drilled with WBM or OBM, the appropriateapproximation for the current I′ is used in the following analysis.

The 3-axis magnetometer 58 in the second well 16 is located at(x,y,z)=(0,0,z₀) and measures the magnetic field components produced bythe current returning on the target casing 18 in the first well 14. Tosimplify the notation the subscript “1” is not shown hereafter, but itis understood that the following magnetic field refers to that producedby the first well 14, namely B(0,0,z₀)=Bx(0,0,z₀){circumflex over(x)}=By(0,0,z₀)ŷ=Bz(0,0,z₀){circumflex over (z)}. For simplicity, theEarth's magnetic field is neglected in the following analysis, and theBHA 22 in the second well 16 is not rotating. These limitations can beremoved. For example, an alternating current will produce an alternatingmagnetic field that can be differentiated from the Earth's staticmagnetic field. Alternatively, the source current can be turned on andoff, and reversed in direction as previously described. Also, if the BHA22 in the second well 16 is rotating at a known frequency, then one cantransform the magnetometer data from the rotating tool frame to thestationary Earth frame.

The magnetic field components are transmitted in real time to thesurface by the MWD tool. By measuring the direction and magnitude of Bwith the magnetometers in the BHA in well #2, and by estimating thecurrent I′ on the casing in well #1, it is possible to determine thedistance between the two wells and their relative positions andorientations.

Provided that the current I′ doesn't vary too much opposite themagnetometer, the magnetic field is given approximately by

$\begin{matrix}{{{\overset{\_}{B}(z)} = {\frac{\mu_{0}I^{\prime}}{2\;\pi\; r^{2}}\hat{n}{x\left( {- \overset{\_}{\overset{\_}{r}}} \right)}}},} & (1)\end{matrix}$where μ₀=4π·10⁻⁷ Henry/m. Here, r is a vector that points from themagnetometers in well #2 to the nearest point on cased well #1. Thisformula assumes a relatively constant current along the casing in well#1. This assumption is correct for OBM since the source current I(z) isconstant along the BHA, and thus the return current I′ will be constanton the casing in the vicinity of the magnetometer. In WBM, I(z) variesalong the BHA, and hence I′ is not constant along the casing. However,if the two wells are separated a distance r much less than L, then I′should not vary too much near the magnetometer. Thus the above formulafor the magnetic field is still useful.

Another analytic expression for the magnetic field for the WBM case thatmay include the variation of current with distance, i.e.I′(z)≈−I(z)≈−I(0)·(L−|z|)/L. This current distribution is characteristicof a linear electric dipole antenna in a conductive medium. An analyticexpression for the magnetic field can be found in Jackson's ClassicalElectrodynamics, published by John Wiley & Sons, Inc., 1967, pages271-273. An analysis can be performed using the expression fromJackson's book, which follows lines similar to that presented here.However, the basic concept is adequately described by the simplerequation for a line current. It is understood that the inventionincludes using different formula, and that the expression presented hereis used solely as an example.

Alternatively, the currents on the BHA 22 and target casing 18 and theresulting magnetic fields can be modeled using a three dimensionalnumerical code, which allows one to specifically include the drillstring, the casing, the borehole, the borehole fluid, and variousformation properties, such as bedding. In a numerical approach, acomputer model is used to simulate the current distributions on the BHA,in the formation, and on the casing, and to computer the resultingmagnetic fields. Comparing the modeled results for the magnetic fieldsto the measured results allows one to estimate the distance anddirection to the cased well. An example of such a numerical code used tomodel SAGD wells is presented later.

assume that the first well penetrates the x−y plane defined by z=Z₀ atthe location (x₀,y₀,z₀) with

$\frac{y_{0}}{x_{0}} = {\tan\;\gamma_{0}}$as shown in FIG. 11. The goal is to determine the quantities: x₀, y_(n),θ, and φ which define the position and direction of cased first wellwith respect to the BHA in the second well. The measured or knownquantities are: I(0), z₀, and B(0,0,z₀). A mathematical analysis resultsin the following equations for the magnetic field components due to acurrent I′ on the target casing in the first well,

$\begin{matrix}{{{B\;{x\left( {0,0,z_{0}} \right)}} = {\frac{\mu_{0}I^{\prime}}{2\;\pi\; r_{0}^{2}}y_{0}\cos\;\phi}},} & (2) \\{{{B\;{y\left( {0,0,z_{0}} \right)}} = {\frac{\mu_{0}I^{\prime}}{2\;\pi\; r_{0}^{2}}x_{0}\cos\;\phi}},{and}} & (3) \\{{{B\;{z\left( {0,0,z_{0}} \right)}} = {\frac{\mu_{0}I^{\prime}}{2\;\pi\; r_{0}^{2}}\left( {{x_{0}\sin\;\theta} - {y_{0}\cos\;\theta}} \right)\sin\;\phi}},{where}} & (4) \\{{r_{0} = \sqrt{x_{0}^{2} + y_{0}^{2} - \beta_{0}^{2}}},{{{and}\mspace{14mu}\beta_{0}} = {\left( {{{- x_{0}}\cos\;\theta} + {y_{0}\sin\;\theta}} \right)\sin\;{\phi.}}}} & \left( {{5a},b} \right)\end{matrix}$

For properly drilled SAGD wells, |By(0,0z₀) | will be much larger that|Bx(0,0,z₀)| or |Bz(0,0,z₀)|. The relative position and direction of thefirst well can be deduced from these quantities using the aboveequations. The angle γ₀ is determined by the ratio of Bx to By, with

$\begin{matrix}{\frac{B_{x}}{B_{y}} = {{{- \tan}\;\gamma_{0}} = {- \frac{y_{0}}{x_{0}}}}} & (6)\end{matrix}$thus eliminating one unknown quantity. If Bx≠0, then γ₀≠0, and the firstwell is not directly below the second well. The horizontal displacement(y₀) is determined once the vertical separation of the wells (x₀) hasbeen found. The ratio of Bz to By gives

$\begin{matrix}{\frac{{B\; z}\;}{B\; y} = {{\left( {{{- x_{0}}\sin\;\theta} + {y_{0}\cos\;\theta}} \right)\tan\;\phi} = {{x_{0}\left( {{\tan\;\gamma_{0}\cos\;\theta} - {\sin\;\theta}} \right)}\tan\;{\phi.}}}} & (7)\end{matrix}$If Bz≠0, then it is likely that φ≠0 and the two wells are not parallel.Finally, By and I′ are related to the inter-well spacing by

$\begin{matrix}{{r_{0}^{2} = {\frac{\mu_{0}I^{\prime}}{2\;\pi\; B\; y}x_{0}\cos\;\phi}},} & (8)\end{matrix}$

Equations 5 a and 5 b can be used to eliminate r₀ ² from equation (8),giving

$\begin{matrix}{{{x_{0}^{2}\left\lbrack {1 - {\sin^{2}{\phi\left( {{{- \cos}\;\theta} + {\tan\;\gamma_{0}\sin\;\theta}} \right)}^{2}}} \right\rbrack} + y_{0}^{2}} = {\frac{\mu_{0}I^{\prime}}{2\pi\; B\; y}x_{0}\cos\;{\phi.}}} & (9)\end{matrix}$The three equations (6), (7), and (9) relate the four unknownquantities, x₀, y₀, θ, and φ. There are three equations in fourunknowns, so there is not a unique solution for the general case witharbitrary angles and well placements. However, only the data from onesingle location along the {circumflex over (z)} axis has been used sofar. Measurements at two locations along the {circumflex over (z)} axisprovide sufficient data to determine all unknown quantities.

For nearly parallel SAGD wells, it is useful to make the small angleapproximation, cos φ≈1, and sin φ≈φ. The normal MWD direction andinclination measurements are sufficiently accurate for the second wellto be drilled in the same direction as the second well within a fewdegrees of error. For example, a relative error of 5° corresponds toφ=0.09. Hence, with the approximations that cos φ≈1 and sin φ≈φ,equations (7) and (9) reduce to:

$\begin{matrix}{\frac{B\; z}{B\; y} \approx {{x_{0}\left( {{\tan\;\gamma_{0}\cos\;\theta} - {\sin\;\theta}} \right)}\phi}} & (10) \\{{x_{0}^{2} + y_{0}^{2}} \approx {{- \frac{\mu_{0}I^{\prime}}{2\;\pi\; B\; y}}{x_{0}.}}} & (11)\end{matrix}$Equation (11) can be rewritten to determine the vertical separation ofthe wells,

$\begin{matrix}{{x_{0} \approx {- \frac{\mu_{0}I^{\prime}}{2{\pi\left\lbrack {1 + \left( \frac{Bx}{By} \right)^{2}} \right\rbrack}{By}}}},} & (12)\end{matrix}$Equations (6) provides the y coordinate

$\begin{matrix}{y_{0} = {\frac{\mu_{0}I^{\prime}{Bx}}{2{\pi\left\lbrack {1 + \left( \frac{Bx}{By} \right)^{2}} \right\rbrack}({By})^{2}}.}} & (13)\end{matrix}$Thus, for cos φ≈1, these coordinates (x₀,y₀, z₀) define one point forthe axis of the first well, based on measurements were made at onemagnetometer location, (0,0,z₀).

The angles θ and φ can be determined from magnetometer measurements at asecond point (0,0,z₀). The two readings may be obtained using twodifferent magnetometers in the BHA, or by moving a single magnetometerbetween the two locations. Repeating the above process yields a secondcoordinate for the first well at (x₁,y₁,z₁), where x₁ and y₁ areobtained from equations (12) and (13), and where B(0,0,z₁) is usedinstead of B(0,0,z₀). The two resulting coordinates, (x₀,y₀,z₀) and(x₁,y₁,z₁), define the axis of well #1: hence θ and φ are determined via

$\begin{matrix}{{{\tan\;\theta} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}},{and}} & (14) \\{{\tan\;\phi} = \sqrt{\frac{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2}}{\left( {z_{1} - z_{0}} \right)^{2}}}} & (15)\end{matrix}$Thus, all of the desired quantities describing the location anddirection of the second well with respect to the first well areobtained.

It is also possible to deduce some directional information about well #2from measurements at a single point. Referring to equation (10), the twoangles θ and φ are related via

$\begin{matrix}{{\delta = \left( {{\tan\;\gamma_{0}\cos\;\theta} - {\sin\;\theta}} \right)}{\phi \approx {- {{\frac{2\pi\;{Bz}}{\mu_{0}I^{\prime}}\left\lbrack {1 + \left( \frac{Bx}{By} \right)^{2}} \right\rbrack}.}}}} & (16)\end{matrix}$The right hand side contains measured values. If Bz=0, then δ=0 whichimplies that eitherφ=0, or  (17)tan θ=tan γ₀

θ=γ₀=nπ  (18)The first condition (16) indicates that the two wells are exactlyparallel, which is the desired conditions for SAGD wells. The secondcondition (17) implies that the directional vector {circumflex over (n)}lies in a plane defined by the {circumflex over (z)} axis and(x₀,y₀,z₀). Equation (18) can be satisfied if the wells are notparallel, but they must both lie in the same plane. In this case, theymight be diverging from, or converging toward each other.

If Bz≠0, then δ≠0, and both of the following conditions must be true:φ≠0, and  (19)tan γ₀ cos θ=sin θ≠0  (20)Equation (19) indicates that the two wells are not parallel, andequation (20) indicates that the directional vector {circumflex over(n)} does not lie in a plane defined by the {circumflex over (z)} axisand (x₀,y₀,z₀). Hence a non-zero value for δ can be used as an errorindication and this can be used in a feedback loop to control thedirection the second well is being drilled.

To illustrate, suppose γ₀=0, so that the second well is exactly abovethe first well at the point (x₀,0,z₀), as shown in FIG. 12. Equation(16) reduces toδ=−φ sin θ  (21)Note that the component of {circumflex over (n)} that lies along the ŷdirection isn_(y)={circumflex over (n)}□ŷ=sin φ sin θ≈φ sin θ  (22)Hence the quantity δ is a direct measurement of the misalignment of thetwo wells with respect to the ŷ direction. A tendency to drift to theleft or right would be detected by monitoring δ, and subsequentlycorrected. However, δ cannot indicate a drift upwards or downwards.

In the general case when tan γ₀≠0, the quantity δ is still useful as afeedback correction. In this case, it corresponds to the portion of{circumflex over (n)} that is perpendicular to the plane defined by the{circumflex over (z)} axis and the point (x₀,y₀,z₀). For example supposetan γ₀=0.4, corresponding to γ₀=0.381 or 21.8°. Referring to FIG. 13,which is a plot of (tan γ₀ cos θ−sin θ), the zero-crossing occurs at21.8°, so that driving δ to zero will bring the two wells into the planedefined by the {circumflex over (z)} axis and the point (x₀,y₀,z₀).

An automatic feedback and control system can be implemented downhole tosteer the second well. Assume that initially the two wells have theproper inter-well spacing (r=d), parallel trajectories (φ=0), and thesecond well is above the first well (γ₀=0), so that the error signal δis zero. If δ deviates from zero, this indicates a left-to-righttendency. The direction of the second well could be changed to bring δback to zero and hence correct the left-to-right drift. Since thiscorresponds to simply driving Bz to zero, it does not require anyadditional information downhole. A downhole processor in the BHA of thesecond well would be able to monitor Bz and control the direction tomaintain the two wells in the same plane.

However, there remains the possibility that the two wells could drifttowards each other or away from each other. The correct spacing can beobtained by monitoring the amplitude of By. From equation (12),

$\begin{matrix}{x_{0} \approx {- {\frac{\mu_{0}I^{\prime}}{2\pi\;{By}}.}}} & (23)\end{matrix}$With I′ constant, a change in By can be interpreted as a change inspacing. The difference in By from its desired value may be used as anerror signal. A processor in the BHA of the second well would be able tomonitor By and Bz and automatically control the separation of the twowells.

This preceding analysis is meant to illustrate the principles, not tolimit the invention. The simplifying assumptions for the current andmagnetic field are not essential to the method. For example, analternative approach is to use a fully three dimensional modeling codeto predict the currents and magnetic field as a function of the wellspacing, the relative well orientation, the details of the BHA andcasing, and varying formation properties. A commercially availableelectromagnetic modeling code, such as Comsol Multiphysics, can be usedto calculate the currents and magnetic field. The procedure is: 1) modela variety of realistic conditions (e.g. well spacing, well orientation,formation resistivity, borehole diameter, mud resistivity, BHA diameterand length, casing diameter, etc.), 2) compare the model results withthe real time measurements, 3) determine the relative orientation andinter-well spacing, and 4) correct the trajectory of the well beingdrilled.

For example, a three dimensional numerical calculation for a 6.75-inch(0.172 m) diameter BHA is shown in FIGS. 14 and 15. The length of BHAbelow the insulated gap is 40 feet (12.2 m), and the length of theinsulated gap is 28-inches (0.71 m). The casing in the first well is12-inches in diameter (0.305 m). The formation resistivity is 10 ohm-nmand WBM is assumed. The current generated across the gap I(0) is 1 amp.

In FIG. 14, the magnetic field components are calculated for the casewhen the second well is parallel to the first well (φ=0) and exactlyabove it (y₀=0). There are two inter-well separations modeled, 16.4 feet(5 m) and 32.8 ft (10 m). The case with no casing present has also beenmodeled. The magnetic field is calculated as a function of z₀ along theBHA. Each data point corresponds to the potential position of themagnetometer in the BHA. When there is no casing present, the threecomponents of the magnetic field are zero, as expected since the currentreturns symmetrically though the formation. When a casing is present inthe first well, Bx(0,0,z)=Bz(0,0,z)=0 as predicted by equations 2 and 4.The only component of magnetic field is By(0,0,z), whose magnitudedepends on the inter-well spacing. The signal at 5 m spacing isapproximately double the signal at 10 m spacing. Equation 3 gives arough approximation for the magnetic field produced by the numericalmodel

$\begin{matrix}{{{By}\left( {0,0,z_{0}} \right)} \approx \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{Lx}_{\;_{0}}}} & (24)\end{matrix}$The current decreases away from the insulated gap, and the inter-wellspacing, x₀, can be deduced from the magnitude.

In FIG. 15, the second well is cased and is not parallel to the firstwell, but is tilted at different angles, φ. The second well intersectsthe z=0 plane at (x,y,z)=(x₀,0,0), i.e. it intersects the x-axis. Thesecond well is parallel to the y−z plane, with θ=π/2. The wells areseparated by 16.4 feet (5 m). The three components of the magnetic fieldcalculated with a three dimensional numerical model also follow theshapes predicted by equations 2, 3, and 4. Note that x₀ is a constant,while y and z vary. In particular, y=z tan φ, so that y is the dependentvariable, and z is an independent variable for a given value of φ. Theapproximate equations for the magnetic field components become:

$\begin{matrix}{{{{Bx}\left( {0,0,z} \right)} \approx {{- \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{Lr}^{2}}}y\;\cos}}\;{{\phi = {{- \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{L\left( {x_{0}^{2} + {z^{2}\sin^{2}\phi}} \right)}}}z\;\sin\;\phi}},}} & (25) \\{{{{By}\left( {0,0,z} \right)} \approx {{- \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{Lr}^{2}}}x_{0}\;\cos}}{{\phi = {{- \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{L\left( {x_{0}^{2} + {z^{2}\sin^{2}\phi}} \right)}}}x_{0}\;\cos\;\phi}},{and}}} & (26) \\{{{{Bz}\left( {0,0,z} \right)} \approx {{- \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{Lr}^{2}}}x_{0}\;\sin}}{\phi = {{- \frac{\mu_{0}{I(0)}\left( {L - {z}} \right)}{2\pi\;{L\left( {x_{0}^{2} + {z^{2}\sin^{2}\phi}} \right)}}}x_{0}\;\sin\;{\phi.}}}} & (27)\end{matrix}$The magnitude of Bx(0,0z) scales approximately as cos φ, and isanti-symmetric about z=0. The anti-symmetry results from z changingsign, while the magnitude grows initially with z until the L−|z| termdominates. The magnitude of By(0,0,z₀) and falls off with distance cosφ, but is symmetric about z=0 as expected. It peaks near z=0 and fallsoff with distance as the current decreases. The magnitude of Bz(0,0,z₀)scales approximately as sin φ and is symmetric about z=0 as predicted bythe above formula.

Hence, the three dimensional numerical model produces results thatgenerally consistent with the much simpler analytic model derived here.The three dimensional numerical model can be used to create a databaseconsisting of magnetic field components versus various conditions (wellspacing, well orientation, casing size, BHA length and diameter,formation resistivity, etc.). This database can then be used to createequations relating the various parameters to the magnetic field. Forexample, the form of such equations might resemble equations 25, 26, and27. The measured magnetic fields can then be used to invert for thedesired parameters, particularly the inter-well spacing and the relativeorientation of the two wells. An independent measurement of theformation resistivity, for example from an LWD tool, could also be usedto refine the parameters.

From the foregoing detailed description of specific embodiments of theinvention, it should be apparent that an apparatus, system and methodfor locating a target wellbore from a second wellbore during drilling ofthe second wellbore that is novel has been disclosed. Although specificembodiments of the invention have been disclosed herein in some detail,this has been done solely for the purposes of describing variousfeatures and aspects of the invention, and is not intended to belimiting with respect to the scope of the invention. It is contemplatedthat various substitutions, alterations, and/or modifications, includingbut not limited to those implementation variations which may have beensuggested herein, may be made to the disclosed embodiments withoutdeparting from the spirit and scope of the invention as defined by theappended claims which follow.

1. A wellbore tool for locating a target wellbore containing aconductive member from a second wellbore, the tool comprising: anelectric current driver having an insulated gap; and a magnetometerpositioned below the electric current driver, wherein the current drivergenerates an electric current across the gap to the portion of the toolbelow the insulated gap, and wherein the magnetometer is configured torespond to a magnetic field induced by a current flowing in theconductive member in the target wellbore.
 2. The tool of claim 1,wherein the electric current is a low frequency current.
 3. The tool ofclaim 1, further including a hollow tubular positioned between themagnetometer and the electric current driver.
 4. The tool of claim 3,wherein the electric current is a low frequency current.
 5. The tool ofclaim 4, further including a measurement-while-drilling tool.
 6. Thetool of claim 1, wherein the magnetometer is a three-axis magnetometer.7. The tool of claim 1, further including a measurement-while-drillingtool.
 8. The tool of claim 1, wherein the magnetometer is positionedwithin a non-magnetic housing that is disposed within a non-magnetictubular.
 9. The tool of claim 1, further including: a drill bit; and asteerable system.
 10. The tool of claim 9, further including a hollowtubular positioned between the magnetometer and the electric currentdriver.
 11. The tool of claim 9, further including ameasurement-while-drilling tool.
 12. The tool of claim 11, wherein themagnetometer is a three-axis magnetometer.
 13. A wellbore tool forlocating a target wellbore containing a conductive member from a secondwellbore and directing the trajectory of the second wellbore relative tothe target wellbore, the tool comprising: an electric current driverhaving an insulated gap; a three-axis magnetometer positioned within anon-magnetic housing that is disposed within a non-magnetic tubular, thethree-axis magnetometer positioned below the electric current driver; adrill bit positioned below the three-axis magnetometer; a hollow tubularconnected between the electric current driver and the three-axismagnetometer; and a measurement-while-drilling tool: wherein the currentdriver generates an electric current across the gap to the portion ofthe tool below the insulated gap, and wherein the three-axismagnetometer is configured to respond to a magnetic field induced by acurrent flowing in the conductive member in the target wellbore.
 14. Amethod of locating a target wellbore containing a conductive member froma second wellbore and directing the trajectory of the second wellborerelative to the target wellbore, the method comprising the steps of:providing a bottom hole assembly having an electric current driver withan insulated gap, a three-axis magnetometer positioned below theelectric current driver, and a drill bit positioned below the three-axismagnetometer; drilling a second wellbore spaced from the target wellborewith the bottom hole assembly; producing a low frequency current flowingfrom the current driver; measuring a magnetic field produced from thetarget wellbore at the bottom hole assembly in the second wellbore; anddetermining a position of the second wellbore relative to the targetwellbore.
 15. The method of claim 14, wherein the step of measuring thetarget magnetic field is performed while drilling the second wellborewith the bottom hole assembly.
 16. The method of claim 15, wherein thestep of measuring the target magnetic field is performed while drillingthe second wellbore with the bottom hole assembly.
 17. The method ofclaim 14, wherein the low frequency flows across the insulated gap tothe portion of the bottom hole assembly below the insulated gap to theconductive material in the target wellbore returning to a portion of thebottom hole assembly above the insulated gap thereby producing a targetmagnetic field.
 18. The method of claim 14, further comprising measuringthe earth's magnetic field, and wherein determining the position of thesecond wellbore comprises determining the position of the secondwellbore from the target magnetic field measurement and the earth'smagnetic field measurements.
 19. The method of claim 14, furthercomprising steering the bottom hole assembly to drill the secondwellbore along a trajectory relative to the target wellbore.
 20. Themethod of claim 14, further comprising measuring a current flowingthrough the bottom hole assembly, and wherein determining the positionof the second wellbore comprises determining the position of the secondwellbore from the target magnetic field measurement and the currentflowing through the bottom hole assembly.
 21. The method of claim 20,wherein determining the position of the second wellbore comprises usingthe following system of equations:${\frac{Bx}{By} = {{{- \tan}\;\gamma_{0}} = {- \frac{y_{0}}{x_{0}}}}};$${\frac{Bz}{By} = {{\left( {{{- x_{0}}\sin\;\theta} + {y_{0}\cos\;\theta}} \right)\tan\;\phi} = {{x_{0}\left( {{\tan\;\gamma_{0}\cos\;\theta} - {\sin\;\theta}} \right)}\tan\;\phi}}};$${{x_{0}^{2}\left\lbrack {1 - {\sin^{2}{\phi\left( {{{- \cos}\;\theta} + {\tan\;\gamma_{0}\sin\;\theta}} \right)}^{2}}} \right\rbrack} + y_{0}^{2}} = {{- \frac{\mu_{0}I^{\prime}}{2\pi\;{By}}}x_{0}\cos\;{\phi.}}$22. The method of claim 14, further comprising: measuring a currentflowing through the bottom hole assembly; and measuring the earth'smagnetic field, and wherein determining the position of the secondwellbore comprises determining the position of the second wellbore fromthe target magnetic field measurement, the current measurement, and theearth's magnetic field measurement.